Predicting the kinetics of a chemical reaction is a challenging task, particularly for systems in states far from equilibrium. This work discusses the use of a relatively new theory known as intrinsic quantum thermodynamics (IQT) and its mathematical framework steepest-entropy-ascent quantum thermodynamics (SEA-QT) to predict the reaction kinetics at atomistic levels of chemically reactive systems in the non-equilibrium realm. IQT has emerged over the last three decades as the theory that not only unifies two of the three theories of physical reality, namely, quantum mechanics (QM), and thermodynamics but as well provides a physical basis for both the entropy and entropy production. The SEA-QT framework is able to describe the evolution in state of a system undergoing a dissipative process based on the principle of steepest-entropy ascent or locally-maximal-entropy generation. The work presented in this dissertation demonstrates for the first time the use of the SEA-QT framework to model the evolution in state of a chemically reactive system as its state relaxes to stable equilibrium. This framework brings a number of benefits to the field of reaction kinetics. Among these is the ability to predict the unique non-equilibrium (kinetic) thermodynamic path which the state of the system follows in relaxing to stable equilibrium. As a consequence, the reaction rate kinetics at every instant of time is known as are the chemical affinities, the reaction coordinates, the direction of reaction, the activation energies, the entropy, the entropy production, etc. All is accomplished without any limiting assumption of stable or pseudo-stable equilibrium. The objective of this work is to implement the SEA-QT framework to describe the chemical reaction process as a dissipative one governed by the laws of quantum mechanics and thermodynamics and to extract thermodynamic properties for states that are far from equilibrium. The F+H2-->HF+H and H+F2-->HF+F reaction mechanisms are used as model problems to implement this framework. / Ph. D.

In this dissertation, applications of thermodynamics at the macroscopic and quantum levels of description are developed. Within the macroscopic level, an upper-level Sustainability Assessment Framework (SAF) is proposed for evaluating the sustainable and resilient synthesis/design and operation of sets of small renewable and non-renewable energy production technologies coupled to power production transmission and distribution networks via microgrids. The upper-level SAF is developed in accord with the four pillars of sustainability, i.e., economic, environmental, technical and social. A superstructure of energy producers with a fixed transmission network initially available is synthesized based on the day with the highest energy demand of the year, resulting in an optimum synthesis, design, and off-design network configuration. The optimization is developed in a quasi-stationary manner with an hourly basis, including partial-load behavior for the producers. Since sustainability indices are typically not expressed in the same units, multicriteria decision making methods are employed to obtain a composite sustainability index. Within the quantum level of description, steepest-entropy-ascent quantum thermodynamics (SEA-QT) is used to model the phenomenon of decoherence. The two smallest microscopic composite systems encountered in Nature are studied. The first of these is composed of two two-level-type particles, while the second one is composed of a two-level-type particle and an electromagnetic field. Starting from a non-equilibrium state of the composite and for each of the two different composite systems, the time evolution of the state of the composite as well as that of the reduced and locally-perceived states of the constituents are traced along their relaxation towards stable equilibrium at constant system energy. The modeling shows how the initial entanglement and coherence between constituents are reduced during the relaxation towards a state of stable equilibrium. When the constituents are non-interacting, the initial coherence is lost once stable equilibrium is reached. When they are interacting, the coherence in the final stable equilibrium state is only that due to the interaction. For the atom-photon field composite system, decoherence is compared with data obtained experimentally by the CQED group at Paris. The SEA-QT method applied in this dissertation provides an alternative and comprehensive explanation to that obtained with the "open system" approach of Quantum Thermodynamics (QT) and its associated quantum master equations of the Kossakowski-Lindblad-Gorini-Sudarshan type. / Ph. D.

In this research, a first-principles, non-equilibrium thermodynamic-ensemble approach applicable across all temporal and spatial scales is developed based on steepest-entropy-ascent quantum thermodynamics (SEAQT). The SEAQT framework provides an equation of motion consisting of both reversible mechanical dynamics and irreversible relaxation dynamics, which is able to describe the evolution of any state of any system, equilibrium or non-equilibrium. Its key feature is that the irreversible dynamics is based on a gradient dynamics in system state space instead of the microscopic mechanics of more traditional approaches. System energy eigenstructure and density operator (or ensemble probability distribution) describe the system and system thermodynamic state, respectively. Extensive properties (i.e., energy, entropy, and particle number) play a key role in formulating the equation of motion and in describing non-equilibrium state evolutions. All the concepts involved in this framework (i.e., eigentstructure, density operator, and extensive properties) are well defined at all temporal and spatial scales leading to the extremely broad applicability of SEAQT. The focus of the present research is that of developing non-equilibrium thermodynamic models based specifically on the irreversible part of the equation of motion of SEAQT and applying these to the study of pure relaxation processes of systems in non-equilibrium states undergoing chemical reactions and heat and mass diffusion. As part of the theoretical investigation, the new concept of hypo-equilibrium state is introduced and developed. It is able to describe any non-equilibrium state going through a pure relaxation process and is a generalization of the concept of stable equilibrium of equilibrium thermodynamics to the non-equilibrium realm. Using the concept of hypo-equilibrium state, it is shown that non-equilibrium intensive properties can be fundamentally defined throughout the relaxation process. The definition of non-equilibrium intensive properties also relies on various ensemble descriptions of system state. In this research, three SEAQT ensemble descriptions, i.e., the canonical, grand canonical, and isothermal-isobaric, are derived corresponding, respectively, to the definition of temperature, chemical potential, and pressure. To computationally and not just theoretically permit the application of the SEAQT framework across all scales, a density of states method is developed, which is applicable to solving the SEAQT equation of motion for all types of non-equilibrium relaxation processes. In addition, a heterogeneous multiscale method (HMM) algorithm is also applied to extend the application of the SEAQT framework to multiscale modeling. Applications of this framework are given for systems involving chemical kinetics, the heat and mass diffusion of indistinguishable particles, power cycles, and the complex, coupled reaction-diffusion pathways of a solid oxide fuel cell (SOFC) cathode. / Ph. D.

Intrinsic quantum Thermodynamics (IQT) is a theory that unifies thermodynamics and quantum mechanics into a single theory. Its mathematical framework, steepest-entropy-ascent quantum thermodynamics (SEAQT), can be used to model and describe the non-equilibrium phenomenon of diffusion based on the principle of steepest-entropy ascent. The research presented in this dissertation demonstrates the capability of this framework to model and describe diffusion at atomistic levels and is used here to develop a non-equilibrium-based model for an isolated system in which He3 diffuses in He4. The model developed is able to predict the non-equilibrium and equilibrium characteristics of diffusion as well as capture the differences in behavior of fermions (He3) and bosons (He4). The SEAQT framework is also used to develop the transient and steady-state model for an open system in which oxygen diffuses through a tin anode. The two forms of the SEAQT equation of motion are used. The first, which only involves a dissipation term, is applied to the state evolution of the isolated system as its state relaxes from some initial non-equilibrium state to stable equilibrium. The second form, the so-called extended SEAQT equation of motion, is applied to the transient state evolution of an open system undergoing a dissipative process as well mass-interactions with two mass reservoirs. In this case, the state of the system relaxes from some initial transient state to steady state. Model predictions show that the non-equilibrium thermodynamic path that the isolated system takes significantly alters the diffusion data from that of the equilibrium-based models for isolated atomistic-level systems found in literature. Nonetheless, the SEAQT equilibrium predications for He3 and He4 capture the same trends as those found in the literature providing a point of validation for the SEAQT framework. As to the SEAQT results for the open system, there is no data in the literature with which to compare since the results presented here are completely original to this work. / Ph. D.

Steepest-entropy-ascent quantum thermodynamics (SEAQT) is a mathematical and theoretical framework for intrinsic quantum thermodynamics (IQT), a unified theory of quantum mechanics and thermodynamics. In the theoretical framework, entropy is viewed as a measure of energy load sharing among available energy eigenlevels, and a unique relaxation path of a system from an initial non-equilibrium state to a stable equilibrium is determined from the greatest entropy generation viewpoint. The SEAQT modeling has seen a great development recently. However, the applications have mainly focused on gas phases, where a simple energy eigenstructure (a set of energy eigenlevels) can be constructed from appropriate quantum models by assuming that gas-particles behave independently. The focus of this research is to extend the applicability to solid phases, where interactions between constituent particles play a definitive role in their properties so that an energy eigenstructure becomes quite complicated and intractable from quantum models. To cope with the problem, a highly simplified energy eigenstructure (so-called ``pseudo-eigenstructure") of a condensed matter is constructed using a reduced-order method, where quantum models are replaced by typical solid-state models. The details of the approach are given and the method is applied to make kinetic predictions in various solid-state phenomena: the thermal expansion of silver, the magnetization of iron, and the continuous/discontinuous phase separation and ordering in binary alloys where a pseudo-eigenstructure is constructed using atomic/spin coupled oscillators or a mean-field approximation. In each application, the reliability of the approach is confirmed and the time-evolution processes are tracked from different initial states under varying conditions (including interactions with a heat reservoir and external magnetic field) using the SEAQT equation of motion derived for each specific application. Specifically, the SEAQT framework with a pseudo-eigenstructure successfully predicts: (i) lattice relaxations in any temperature range while accounting explicitly for anharmonic effects, (ii) low-temperature spin relaxations with fundamental descriptions of non-equilibrium temperature and magnetic field strength, and (iii) continuous and discontinuous mechanisms as well as concurrent ordering and phase separation mechanisms during the decomposition of solid-solutions. / Ph. D. / Many engineering materials have physical and chemical properties that change with time. The tendency of materials to change is quantified by the field of thermodynamics. The first and second laws of thermodynamics establish conditions under which a material has no tendency to change; these conditions are called equilibrium states. When a material is not in an equilibrium state, it is able to change spontaneously. Classical thermodynamics reliably identifies whether a material is susceptible to change, but it is incapable of predicting how change will take place or how fast it will occur. These are kinetic questions that fall outside the purview of thermodynamics. A relatively new theoretical treatment developed by Hatsopoulos, Gyftopoulos, Beretta and others over the past forty years extends classical thermodynamics into the kinetic realm. This framework, called steepest-entropy-ascent quantum thermodynamics (SEAQT), combines the tools of thermodynamics with quantum mechanics through a postulated equation of motion. Solving the equation of motion provides a kinetic description of the path a material will take as it changes from a non-equilibrium state to stable equilibrium. To date, the SEAQT framework has been applied primarily to systems of gases. In this dissertation, solid-state models are employed to extend the SEAQT approach to solid materials. The SEAQT framework is used to predict the thermal expansion of silver, the magnetization of iron, and the kinetics of atomic clustering and ordering in binary solid-solutions as a function of time or temperature. The model makes it possible to predict a unique kinetic path from any arbitrary, non-equilibrium, initial state to a stable equilibrium state. In each application, the approach is tested against experimental data. In addition to reproducing the qualitative kinetic trends in the cases considered, the SEAQT framework shows promise for modeling the behavior of materials far from equilibrium.